For the first time, the city’s five police unions have agreed to lock arms in labor negotiations with the city to prevent a repeat of the “zeroes for heroes” no-raise provision in the last contract, The Post has learned.

The five union presidents have privately agreed to allow the city’s largest police union, the Patrolmen’s Benevolent Association, to take the lead in talks with the Giuliani administration, officials say.

The strategy could be critical, because the last round of contract talks was marred by a break within their ranks and the unions ultimately swallowing a controversial five-year contract that gave no pay raises for two years.

The political fallout from the contract, which hurt police morale and created a rift between the PBA and City Hall, also led to a stunning vote to oust the PBA’s leadership and replace it with a new team headed by President Patrick Lynch.

Lynch believes the cop union is in a strong bargaining position, thanks to the city’s historic crime decline, which has fueled the housing market and a booming tourist industry that pumps hundreds of millions of dollars into city coffers.

“The reason New York City is in such a good shape, in terms of safety and finances, is the work my membership has done,” Lynch said, noting that the mayor and City Council members gave themselves hefty pay raises recently.

The union leaders believe the mayor’s expected run for Senate may work to their advantage in these negotiations, and vow to use their political muscle at the ballot box, as they did in defeating the proposed City Charter revisions last week.

“We will be a player [in next year’s election],” Lynch declared. “And when we put out our endorsement, it goes a long way.”

Tony Garvey, the president of the Lieutenant Benevolent Association who broke ranks with his counterparts during the last negotiations, agrees his members should benefit this time by letting the PBA take the lead.

Thomas Scotto, the detectives president who has spearheaded the coalition, said his members, too, stand a better chance of winning improved pension and welfare benefits.

“We cannot function [as a bargaining entity] if we do not have a cohesive group,” Scotto said.

The captains and sergeants unions round out the coalition.

Deputy Mayor Randy Levine said the city welcomes opening negotiations, but the unions should not count on “politics” playing any role in how the city bargains with them.